I think there must be a misprint there in your English version:
The girl signs for the weary soldier is praised

However, if it was 'The girl sings for the weary soldier and is praised' then I think your first translation is spot on, while if the English was 'The girl who sings for the weary soldier is praised' then your second one is correct.

Radek wrote:It can be coniunction, but if it is, tehere must be mistake. This is the 19 chapter of the book and authors does not described coniunction.

I finally looked through the book, scouring chapters 1-20 for nam or enim "for", and you are quite right that you haven't had the word yet. However, beginning on page 270 of the pdf file, there is an English-Latin vocabulary with all the words used in the book. If you look up "for" (page 264 of the book, 274 of the document) you will see the first one has nam and enim and further down there is the dative of course. It isn't necessary for the author to discuss what a conjunction is, because he expects you to know it as a general piece of grammar for any language (which is unfortunate since beginners don't typically know a lot of grammar in modern times). As a matter of fact, you have already been learning some conjunctions which include words like et, aut, cum, ubi, quando, and more.

Whatever the case, I am sure this is not a misprint of the book. It may be that he is trying to make you look up words which he has provided you with, or that he just forgot to put it in the vocabulary for that chapter, but the sentence is certainly sound.

But I know it (this book I use only to master English-Latin easy exercises, I think about N&H but now I think I should proctice with more simple sentences) and think you can be right.

I don't know how much learning you have, but I would imagine that it is impossible to get very far in N&H without a complete familiarity with the fundamentals of Latin grammar and syntax. N&H does not go into very detailed explanations and assumes that you know Latin very well. N&H really just polishes your Latin by adding on small facets of the language that are too minute for a primary textbook to cover. Not only will it be difficult to go through N&H before completing a full grammar course, but you will be learning small things and maybe missing some of the bigger, more important things that the normal textbook had. When you think you are ready for prose composition, go ahead, but this is the kind of thing that even very good students make errors on